Let \(G\)  be a simple connected graph with vertex set \(V(G)\)  and edge set \(E(G)\) , and denote by \(n=|V(G)|\)  and \(m=|E(G)|\)  the number of vertices and edges, respectively. The degree of a vertex \(v\)  in \(G\) , denoted by \(d_G(v)\)  or \(d(u)\) , is the number of its neighbors. If the vertices \(u\)  and \(v\)  are adjacent, then the edge connecting them is labeled by \(e=uv\) . In the mathematical and chemical literature, several dozens of vertex-degree-based (VDB) graph invariants (usually referred to as "topological indices") have been introduced and extensively studied [1]}, [2]}, [3]}, [4]}, [5]}. Their general formula is
\(\begin{split} TI(G)=\sum _{uv\in E}F(d_G(u),d_G(v)),\nonumber \end{split}\) 
